15 June 2006 Fractal characteristics of exoplanet transit time series data
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Exoplanet transit time series photometric data usually contain noise levels that are comparable to the transit signal jumps. The analysis that assumes Gaussian noise and extensive data averaging calibrated to a reference star has been the traditionally used algorithm. This paper studied the fractal property of the time series and found that the fractal dimension changes for time series data that contain transits. The Higuchi fractal method, where the length of the increment in various time lags is plotted against the lags, was used in this study. (Higuchi, T., "Approach to an irregular time series on the basis of fractal theory", Physica D, vol 31, 277-283, 1988). The fractal algorithm was calibrated with the Weierstrass function. Simulations using Gaussian noise suggested that a transit jump signal at about 1-sigma noise level would produce changes in fractal dimension, while non-Gaussian noise simulations suggested a higher transit jump signal. The fractal algorithm was applied to data collected on HD 209458 as well as on published data. The transit caused a fractal dimension change of about 0.06. An over-exposed CCD dataset with much noise was also analyzed and a fractal dimension change of about 0.02 was obtained. The result suggests that fractal dimension analysis, without the assumption of error normality, is an alternative method for identifying transits in time series photometric data.
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George Tremberger, George Tremberger, H. Yao, H. Yao, A. Flamholz, A. Flamholz, E. Cheung, E. Cheung, P. Marchese, P. Marchese, D. Cotten, D. Cotten, D. H. Lieberman, D. H. Lieberman, T. D. Cheung, T. D. Cheung, "Fractal characteristics of exoplanet transit time series data", Proc. SPIE 6265, Space Telescopes and Instrumentation I: Optical, Infrared, and Millimeter, 62653V (15 June 2006); doi: 10.1117/12.672206; https://doi.org/10.1117/12.672206

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